On 10 Mar 2003 at 12:27, Markus Schulze wrote: -snip- > However, according to Steve Eppley, there is a merit > difference. Steve, who uses the term "MAM" for Ranked Pairs
It is more reasonable to use the term MAM as a variation of Ranked Pairs than as a synonym for Ranked Pairs. MAM is monotonic, whereas Zavist-Tideman's Ranked Pairs 1989 is not (nor is the "winning votes" variation of Ranked Pairs 1989). MAM satisfies strong Pareto and clone independence, whereas Tideman's Ranked Pairs 1987 does not. And, being a "winning votes" variation, MAM satisfies some criteria (Minimal Defense, Non-drastic Defense and Truncation Resistance) that "margins" variations of Ranked Pairs do not satisfy. Given its satisfaction of these criteria, MAM seems to be the best variation of Ranked Pairs. > and the term "PathWinner" for the beat path method, writes: > >> MAM may be preferable to PathWinner for a couple of reasons: >> >> 1. MAM (but not PathWinner) satisfies immunity from majority >> complaints (IMC), immunity from second-place complaints (I2C) >> and other criteria described in the document Immunity from >> Majority Complaints. >> >> 2. Computer simulations using randomly generated profiles of >> voters' orderings suggest the alternative chosen by MAM will >> beat pairwise the alternative chosen by PathWinner more often >> than vice versa, and that over the long run more voters will >> prefer MAM winners over PathWinner winners than vice versa. Also, MAM satisfies Peyton Young's criterion "local independence of irrelevant alternatives (LIIA), and BeatpathWinner does not. Call a subset X of the alternatives "contiguous" if no alternative outside X is socially ordered equal to or between any alternatives in X. LIIA: For all subsets X of the alternatives, if X is contiguous then the alternatives in X must be socially ordered, relative to each other, the same as they would be if all alternatives outside X were deleted from the votes. LIIA is weaker than Immunity from Majority Complaints, both described in my web pages. Young wrote in "Equity: In Theory and Practice" that LIIA is a "slight weakening" of Arrow's IIA, and on that basis argued for the Kemeny-Young method. But clearly "LIIA + Clone Independence" is even less of a weakening of IIA, so Young ought to have argued for a method like MAM that satisfies both LIIA and Clone Independence. Personally, I don't think Young's justification of LIIA is as significant as Young thinks, but some readers may consider LIIA satisfaction to be another significant advantage MAM has over BeatpathWinner. (It may also help in a campaign to reform the voting method if one can cite Young's desire for LIIA compliance and point out the proposed voting method satisfies it.) Mike Ossipoff wrote that another MAM advantage is its briefer definition, but since that kind of thing tends like beauty to be in the eye of the beholder, I didn't make that claim in my web pages. Mike seems to like to minimize word count even if that reduces clarity, whereas I think clarity is more important than brevity. * * In a recent message I erred when I said Mike Ossipoff considers MAM best in both committees and public elections, judging by his recent messages in EM that say he thinks it's better in public elections but not in committees. I must have misunderstood the implications of some of his comments in private email, or maybe he's changed his mind again. Maybe I'll find time to reread his private email, and time to argue with him over his claim that the BeatpathWinner algorithm is really briefer or more elegant. These can depend on the language in which the algorithm is written. For instance, languages that include "sorting" as a high level instruction make MAM much briefer and more elegant than languages that demand the programmer implement a sorting routine using low level instructions. To see a fairly brief yet complete MAM algorithm written in "structured English", follow the link to "MAM procedure definition" from "www.alumni.caltech.edu/~seppley". MAM's definition and algorithm can be significantly shortened for public elections, since in that context it is reasonable to ignore the unlikely occurrence of two or more majorities that are exactly the same size, and pairings that are tied. The definition and algorithm can also be shortened in the committee context if, instead of using Random Voter Hierarchy to construct a tiebreaking ordering of the alternatives, we use for the tiebreaking ordering the chronological order in which the alternatives were nominated. This variation doesn't completely satisfy the Neutrality criterion, but rewarding the early alternatives when breaking ties seems a reasonable and slight relaxation of Neutrality. This variation might also not completely satisfy Clone Independence--I won't have time to check this for awhile--but, if not, probably provides enough clone independence. -- Steve Eppley _______________________________________________ Election-methods mailing list [EMAIL PROTECTED] http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com
